Dislocation drag from phonon wind in an isotropic crystal at large velocities

Abstract

The anharmonic interaction and scattering of phonons by a moving dislocation, the photon wind, imparts a drag force $vB(v,T,\rho )$ on the dislocation. In early studies the drag coefficient $B$ was computed and experimentally determined only for dislocation velocities $v$ much less than transverse sound speed, $c_t$. In this paper we derive analytic expressions for the velocity dependence of $B$ up to $c_t$ in terms of the third-order continuum elastic constants of an isotropic crystal, in the continuum Debye approximation, valid for dislocation velocities approaching the sound speed. In so doing we point out that the most general form of the third order elastic potential for such a crystal and the dislocation-phonon interaction requires two additional elastic constants involving asymmetric local rotational strains, which have been neglected previously. We compute the velocity dependence of the transverse phonon wind contribution to $B$ in the range 1%-90% $c_t$ for Al, Cu, Fe, and Nb in the isotropic Debye approximation. The drag coefficient for transverse phonons scattering from screw dislocations is finite as $v\to c_t$, whereas $B$ is divergent for transverse phonons scattering from edge dislocations in the same limit. This divergence indicates the breakdown of the Debye approximation and sensitivity of the drag coefficient at very high velocities to the microscopic crystalline lattice cutoff. We compare our results to experimental results wherever possible and identify ways to validate and further improve the theory of dislocation drag at high velocities with realistic phonon dispersion relations, inclusion of lattice cutoff effects, MD simulation data, and more accurate experimental measurements.

arXiv comment26 pages, 5 figures; v2 minor revision

References in corpus (7)

• Atomistic simulations of dislocation mobility in Al, Ni and Al/Mg alloys
• Supersonic dislocations observed in a plasma crystal
• Dynamic Peierls-Nabarro equations for elastically isotropic crystals
• Velocity dependent dislocation drag from phonon wind and crystal geometry
• Properties of dislocation drag from phonon wind at ambient conditions
• Line tension of a dislocation moving through an anisotropic crystal
• Averaging of elastic constants for polycrystals

Cited by in corpus (9)

• Analytic model of the remobilization of pinned glide dislocations: including dislocation drag from phonon wind
• Dislocation drag and its influence on elastic precursor decay
• Clarifying the definition of 'transonic' screw dislocations
• Limiting velocities and transonic dislocations in Mg
• On the temperature and density dependence of dislocation drag from phonon wind
• A general solution for accelerating screw dislocations in arbitrary slip systems with reflection symmetry
• Comparing theoretical predictions of radiation-free velocities of edge dislocations to molecular dynamics simulations
• Properties of accelerating edge dislocations in arbitrary slip systems with reflection symmetry
• PyDislocDyn: A Python code for calculating dislocation drag and other crystal properties